R-Math Algorithms

A Rust crate for rare, high-performance mathematical algorithms not commonly found in mainstream libraries.

Current Features

• Tonelli-Shanks: Modular square roots (r^2 ≡ n mod p) over prime moduli (constant-time version)

• Cuthill–McKee & Reverse Cuthill–McKee: Bandwidth reduction for sparse symmetric matrices (adjacency list, CSR, and CSC formats)

  • Supports conversion from sprs sparse matrix types

• Freivalds' Algorithm: Fast probabilistic verification of matrix multiplication (scalar, modular, and SIMD-accelerated variants)

• Well-documented, tested, and benchmarked implementations

• SIMD acceleration for Freivalds' algorithm (nightly Rust required)

More about the algorithms here

R-Math Algorithms Overview

Installation

Add to your Cargo.toml:

[dependencies]
rma = "0.1"

Enable SIMD features (nightly Rust required):

[dependencies]
rma = { version = "0.1", features = ["simd"] }

Benchmarks

Benchmarks are provided using criterion in the benches/ directory.

On stable Rust:

• Run all benchmarks:

  cargo bench
  

• Run a specific benchmark (e.g., only Freivalds):

  cargo bench --bench freivalds_bench
  

On nightly Rust (to enable SIMD):

• Run all benchmarks with SIMD:

  cargo bench --features simd
  

• Run a specific benchmark with SIMD:

  cargo bench --bench freivalds_bench --features simd
  

becnhes naming convention is filename with the _bench suffix; you check all in Cargo.toml

Testing

On stable Rust:

• Run all tests:

  cargo test
  

On nightly Rust (to enable SIMD tests):

• Run all tests with SIMD:

  cargo test --features simd
  

Documentation

• API Documentation (docs.rs)

Minimum Supported Rust Version

• Nightly Rust required for SIMD features (#![feature(portable_simd)])
• Stable Rust for scalar and modular algorithms

Roadmap & Contributions

This crate will be updated with new algorithms over time, focusing on rare, advanced, or otherwise unported mathematical algorithms.

License

Licensed under either of

• Apache License, Version 2.0
• MIT license

r-math aims to be a home for rare, advanced, and high-performance mathematical algorithms in Rust.